the equilibrium will be characterized by the seller factoring all of its accounts receivable without recourse and performing zero credit monitoring. However, if the conditions do not
hold, then a seller with a sufficiently low probability of bankruptcy will sell its highest credit quality receivables without recourse, but must resort to the use of recourse in order
to sell both its intermediate and poor credit quality receivables. The equilibrium will be slightly different for sellers which have a high probability of bankruptcy. A seller in this
category will still sell its highest credit quality receivables without recourse, but will be able to sell only its intermediate quality receivables through the use of recourse. Because
of the deleterious impact of the moral hazard problem on the equilibrium price offered by the factor, even the promise of recourse will be insufficient to motivate the sale of the
seller’s lowest quality receivables.
The paper is organized as follows. Section II outlines the assumptions and motivates the model. Section III models the seller’s decision when it keeps its accounts receivable.
Section IV models the seller’s decision to factor its accounts receivable. Section V provides a discussion of the data set, testable implications, and empirical methodology.
Section VI presents the empirical results, and Section VII concludes the paper.
II. The Assumptions and A Generalized Form of the Seller’s Profit Function
Assume that a risk neutral seller has an order on its books to manufacture a product or to provide a service which it will sell for a promised payment of L. The cost to
manufacture the good is 1, which the seller must pay at time t 5 0. The seller finances its initial investment at its internal cost of capital, r
i
. Assume that the manufacturing process is instantaneous and that the seller extends trade credit to its customers.
5
Thus, at time t 5 0
1
, the seller delivers the finished good, but the customer need not pay for the good until the end of the credit extension period, which is assumed to be t periods.
The seller has the capability of credit monitoring its customer at a level c, where c [ [0, `. Credit monitoring is defined to be the ongoing process of expediting payment on
an outstanding invoice so that the invoice will be paid off promptly. The seller’s cost of credit monitoring is given by u times c, where u is some positive constant. The cost is
incurred at the end of the period time t 5 t. A greater c implies that the seller is exerting more expediting pressure on its customer.
The seller knows the payoff distribution of the trade receivable. The random variable x˜
, the realized payment by the customer, is assumed to have a probability distribution which is an increasing function of the level of credit monitoring and the receivable’s credit
quality, a. a [ [1, `, and represents the reciprocal of the perceived a priori probability that the customer will not pay off the receivable within the allocated credit extension
period. Thus, a provides an indication of the customer’s creditworthiness: the greater the a
, the greater the likelihood that the receivable will be paid off in full. It is further assumed that the distribution for the payoff satisfies a strict convexity of
distribution function constraint with respect to the level of credit monitoring, c, and the level of receivable credit quality, a. Thus, the distribution function, F, has the following
property:
5
See Petersen and Rajan 1997 for a detailed discussion and empirical test of the existing theories which attempt to explain the existence of trade credit.
The Economics of Factoring Accounts Receivable 341
F~ x ua, lc 1 ~1 2 lc9 , lF~ xua, c 1 ~1 2 l F~ xua, c9
and F~ x
ula 1 ~1 2 la, c , lF~ xua, c 1 ~1 2 l F~ xua9, c. The strict convexity of distribution function constraint implies that the expected payoff
will be increasing and strictly concave in both a and c.
6
If the seller increases its monitoringexpediting efforts as c increases or the customer’s perceived creditworthi-
ness increases as c increases, the probability that a given receivable will be paid promptly increases. In turn, as the probability that the receivable will be paid off in a
timely fashion increases, so does the receivable’s expected value. Note that the strict concavity of the expected payoff with regard to a and c implies that there will be strictly
decreasing returns to scale in both the receivable’s credit quality and in the seller’s level of monitoring.
At time t 5 0
1
, the seller may sell a fraction b of its receivable to a risk neutral factor, who will pay the seller a discounted amount of the receivable’s face value.
7
Assume that the market for the purchase of receivables is competitive. Both the seller and the factor can
costlessly observe a, the receivable’s credit quality, at time t 5 0. The factor also knows the receivable’s payoff distribution, but is not able to accurately perceive what the seller’s
level of credit monitoring, c, will be. In some cases, the seller may choose to sell its receivable with recourse. Let z be an indicator function that equals 1 if the seller offers
recourse, and 0 otherwise. It is assumed that if the seller offers recourse, then it must offer full recourse i.e., in the event that the seller’s customer defaults on the receivable, the
seller will be liable for the entire delinquent amount.
8
Sopranzetti 1997a argued that the seller may have a higher cost of internal funding than the factor because of tax incentives, underinvestment, or costs related to financial
distress, so we assume that the factor has a cost of internal funding equal to r
f
which is less than r
i
.
9
The factor undertakes a given level of monitoring, m, where m [ [0, ` and is determined optimally by the factor given his cost and efficiency parameters. The cost of
monitoring will be w times m, where w is some positive constant that will be paid at the end of the period. The level of monitoring, m, represents the amount of effort that the
factor expends on expediting prompt payment by the customer on the outstanding receivable. It is assumed that once the factor commits to a given level of monitoring, it
will perform as promised, and that the factor must pay the seller for the receivable at the beginning of the period. The expected payoff when the factor monitors is
L
x dF x
ua, c, m
. Lastly, the factor is able to accurately and costlessly observe p, the seller’s probability of solvency.
The model, as presented above, yields essentially no closed-form, general results; so, in order to obtain useful results, it will be necessary to invoke a specific functional form
for the receivable’s expected payoff. Our chosen functional form for the expected payoff is
L
x dF x
ua, c, m 5 L1 2 1a e
2bc2dm
. Although the paper’s theoretical findings depend crucially upon the chosen functional form, this representation for the receivable’s
6
See Hart and Holmstro¨m 1987 for a proof of this claim.
7
The factor pays the seller at time t 5 01, when the receivable is actually sold.
8
The case of partial recourse can be handled by allowing z [ [0, 1].
9
See Section V.B for empirical justification for this claim.
342 B. J. Sopranzetti
expected payoff seems sensible, because as the credit quality of the receivable increases as a increases, the expected payoff converges to L the face value regardless of how
much credit monitoring is done by the seller or the factor. Also, if zero credit monitoring is performed by both the seller and the factor c 5 0 and m 5 0, then the expected payoff
will be bounded below by L1 2 1a. However, as the level of the seller’s or the factor’s credit monitoring effort increases, then the expected payoff on the receivable converges
at the rate b or d, respectively, to the promised payment, L.
10
Also, as c [ [0, ` and m [ [0, `, it is necessary to constrain the parameters such that Lb . u and Ld . w.
The Generalized Form of the Seller’s Expected Profit Function
The general form of the seller’s expected profit function is: e
2r
i
t
E
L
~1 2 b px 2 zbp~L 2 x dF ~ x ua, c, m 2 e
2r
i
t
upc 2 1
1 e
2r
t
t
b
H
E
L
x 1 zp~L 2 x dF ~ x ua, c, m 2 wm
J
, 1
where the first term is the seller’s expected payoff from keeping a fraction 1 2 b of the receivable minus the seller’s expected liability due to the recourse guarantee; the second
term is the seller’s monitoring cost; the third term is the initial investment; and the last term is the price that is paid to the seller by the factor.
III. The Seller’s Decision To Keep Its Accounts Receivable
